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<div class="ChapSects" ><a href="chap16.html#X7BAE6D0285667B1F" >16 <span class="Heading" >Finite skeletal discrete categories</span ></a>
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap16.html#X7D03633A7D98026B" >16 .1 <span class="Heading" ><strong class="pkg" >GAP</strong > Categories</span ></a>
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<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap16.html#X86FECC7F7B10DFB5" >16 .1 -1 IsFiniteSkeletalDiscreteCategory</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap16.html#X7B0369367B25FF27" >16 .1 -2 IsObjectInFiniteSkeletalDiscreteCategory</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap16.html#X83A994137F28C142" >16 .1 -3 IsMorphismInFiniteSkeletalDiscreteCategory</a></span >
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<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap16.html#X86EC0F0A78ECBC10" >16 .2 <span class="Heading" >Constructors</span ></a>
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<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap16.html#X82D81EB281E4B15F" >16 .2 -1 FiniteSkeletalDiscreteCategory</a></span >
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<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap16.html#X7C701DBF7BAE649A" >16 .3 <span class="Heading" >Attributes</span ></a>
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<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap16.html#X82A86530836AB45F" >16 .3 -1 UnderlyingListOfGapObjects</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap16.html#X83402D288247887B" >16 .3 -2 UnderlyingGapObject</a></span >
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<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap16.html#X871597447BB998A1" >16 .4 <span class="Heading" >Properties</span ></a>
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<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap16.html#X7F7BD8CF86A2D122" >16 .4 -1 IsDiscreteCategory</a></span >
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<h3>16 <span class="Heading" >Finite skeletal discrete categories</span ></h3>
<p><a id="X7D03633A7D98026B" name="X7D03633A7D98026B" ></a></p>
<h4>16 .1 <span class="Heading" ><strong class="pkg" >GAP</strong > Categories</span ></h4>
<p><a id="X86FECC7F7B10DFB5" name="X86FECC7F7B10DFB5" ></a></p>
<h5>16 .1 -1 IsFiniteSkeletalDiscreteCategory</h5>
<div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >an style='color: green'>8227; IsFiniteSkeletalDiscreteCategory</code >( <var class="Arg" >C</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >
<p>Returns: <code class="keyw" >true</code > or <code class="keyw" >false</code ></p>
<p>The <strong class="pkg" >GAP</strong > type of a finite skeletal discrete category.</p>
<p><a id="X7B0369367B25FF27" name="X7B0369367B25FF27" ></a></p>
<h5>16 .1 -2 IsObjectInFiniteSkeletalDiscreteCategory</h5>
<div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >an style='color: green'>8227; IsObjectInFiniteSkeletalDiscreteCategory</code >( <var class="Arg" >O</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >
<p>Returns: <code class="keyw" >true</code > or <code class="keyw" >false</code ></p>
<p>The <strong class="pkg" >GAP</strong > type of an object in a finite skeletal discrete category.</p>
<p><a id="X83A994137F28C142" name="X83A994137F28C142" ></a></p>
<h5>16 .1 -3 IsMorphismInFiniteSkeletalDiscreteCategory</h5>
<div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >an style='color: green'>8227; IsMorphismInFiniteSkeletalDiscreteCategory</code >( <var class="Arg" >M</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >
<p>Returns: <code class="keyw" >true</code > or <code class="keyw" >false</code ></p>
<p>The <strong class="pkg" >GAP</strong > type of a morphism in a finite skeletal discrete category.</p>
<p><a id="X86EC0F0A78ECBC10" name="X86EC0F0A78ECBC10" ></a></p>
<h4>16 .2 <span class="Heading" >Constructors</span ></h4>
<p><a id="X82D81EB281E4B15F" name="X82D81EB281E4B15F" ></a></p>
<h5>16 .2 -1 FiniteSkeletalDiscreteCategory</h5>
<div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >an style='color: green'>8227; FiniteSkeletalDiscreteCategory</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( function )</td ></tr ></table ></div >
<p>Returns: a <strong class="pkg" >CAP</strong > category</p>
<p>Construct a finite skeletal discrete category.</p>
<p><a id="X7C701DBF7BAE649A" name="X7C701DBF7BAE649A" ></a></p>
<h4>16 .3 <span class="Heading" >Attributes</span ></h4>
<p><a id="X82A86530836AB45F" name="X82A86530836AB45F" ></a></p>
<h5>16 .3 -1 UnderlyingListOfGapObjects</h5>
<div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >an style='color: green'>8227; UnderlyingListOfGapObjects</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >
<p>Returns: a list of <strong class="pkg" >CAP</strong > objects</p>
<p>The underlying <strong class="pkg" >GAP</strong > objects of a finite skeletal discrete category.</p>
<p><a id="X83402D288247887B" name="X83402D288247887B" ></a></p>
<h5>16 .3 -2 UnderlyingGapObject</h5>
<div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >an style='color: green'>8227; UnderlyingGapObject</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >
<p>Returns: a <strong class="pkg" >CAP</strong > object </p>
<p>The underlying <strong class="pkg" >GAP</strong > object of an object in a finite skeletal discrete category.</p>
<p><a id="X871597447BB998A1" name="X871597447BB998A1" ></a></p>
<h4>16 .4 <span class="Heading" >Properties</span ></h4>
<p><a id="X7F7BD8CF86A2D122" name="X7F7BD8CF86A2D122" ></a></p>
<h5>16 .4 -1 IsDiscreteCategory</h5>
<div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >an style='color: green'>8227; IsDiscreteCategory</code >( <var class="Arg" >C</var > )</td ><td class="tdright" >( property )</td ></tr ></table ></div >
<p>Returns: <code class="keyw" >true</code > or <code class="keyw" >false</code ></p>
<p>The property of <var class="Arg" >C</var > being a discrete <strong class="pkg" >CAP</strong > category, i.e., equivalent to a category in which any morphism is an identity.</p>
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